The singular integrals (REF ) and () do not lend
themselves easily to evaluation. In particular, it is unlikely that IB points and grid
points will coincide. For a regular grid with spacing \(h\) , we replace the Dirac
\(\) -function with a regularized kernel, \(_h\) , which is a product of
one-dimensional kernels, \(h^{-1}(h^{-1}x)\) . [1]} gives several
options for \(\) . The methods described in this paper do not depend on a particular
\(\) , but we restrict ourselves to the cosine kernel from [2]}.
The cosine kernel is simple to implement, but does not satisfy all of the moment
conditions for a 4-point kernel, though it approximates a kernel with the appropriate
discrete properties.
